Subgroups — C₁₄₉×#18388 #49197337

Order 38144.

1258 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3496×C₁₄₉	C₂	1	1	yes	maximal, characteristic
2	#3206×C₁₄₉	C₂	1	2	yes	maximal, complemented
3	#2563×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#1601×C₁₄₉	C₂	1	8	yes	maximal, complemented
5	#1502×C₁₄₉	C₂	1	2	yes	maximal, complemented
6	#1460×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×H(5,𝔽₂)×C₁₄₉	—	2	1	no	—
8	#547×C₁₄₉	—	2	2	no	—
9	#546×C₁₄₉	—	2	4	no	—
10	D₄²×C₁₄₉	—	2	2	no	—
11	#537×C₁₄₉	—	2	1	no	—
12	#534×C₁₄₉	C₂²	1	4	yes	—
13	#532×C₁₄₉	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
15	C₂×#121×C₁₄₉	—	2	2	no	—
16	C₂×C₄×D₄×C₁₄₉	C₂²	1	1	yes	characteristic
17	#492×C₁₄₉	—	2	2	no	—
18	#487×C₁₄₉	—	2	2	no	—
19	#461×C₁₄₉	—	2	4	no	—
20	#448×C₁₄₉	C₂²	1	8	yes	complemented
21	#431×C₁₄₉	C₂²	1	2	yes	complemented
22	#393×C₁₄₉	C₂²	1	4	yes	complemented
23	#390×C₁₄₉	—	2	1	no	—
24	#382×C₁₄₉	—	2	1	no	—
25	#380×C₁₄₉	—	2	2	no	—
26	C₄×C₄⋊C₄×C₁₄₉	C₂²	1	1	yes	characteristic, complemented
27	#327×C₁₄₉	C₂²	1	8	yes	complemented
28	#323×C₁₄₉	C₂²	1	4	yes	complemented
29	H(5,𝔽₂)×C₁₄₉	—	4	4	no	—
30	H(5,𝔽₂)×C₁₄₉	—	4	4	no	—
31	C₂×#41×C₁₄₉	—	2	4	no	—
32	C₂×#41×C₁₄₉	—	2	2	no	—
33	C₂²×Q₈×C₁₄₉	C₂³	1	2	yes	—
34	C₂²×D₄×C₁₄₉	—	2	4	no	—
35	C₂²×D₄×C₁₄₉	—	2	4	no	—
36	C₂²×D₄×C₁₄₉	—	2	2	no	—
37	C₂²×D₄×C₁₄₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₄₉	D₄	1	2	yes	—
39	C₂×SD₁₆×C₁₄₉	—	2	8	no	—
40	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
41	C₄⋊Q₈×C₁₄₉	—	2	2	no	—
42	C₄⋊Q₈×C₁₄₉	D₄	1	2	yes	—
43	#127×C₁₄₉	D₄	1	2	yes	—
44	#124×C₁₄₉	—	2	2	no	—
45	#123×C₁₄₉	—	2	8	no	—
46	C₂²⋊Q₈×C₁₄₉	—	2	4	no	—
47	#121×C₁₄₉	—	2	4	no	—
48	#121×C₁₄₉	—	2	4	no	—
49	#121×C₁₄₉	—	2	4	no	—
50	#121×C₁₄₉	—	2	2	no	—
51	#121×C₁₄₉	—	2	4	no	—
52	#121×C₁₄₉	C₂³	1	4	yes	—
53	#120×C₁₄₉	—	2	8	no	—
54	C₄×D₄×C₁₄₉	—	2	2	no	—
55	C₄×D₄×C₁₄₉	—	2	2	no	—
56	C₄×D₄×C₁₄₉	—	2	2	no	—
57	C₄×D₄×C₁₄₉	D₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₁₄₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
60	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₁₄₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₁₄₉	D₄	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₄₉	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₄₉	C₂³	1	2	yes	—
66	C₂×C₄²×C₁₄₉	—	2	1	no	—
67	C₂×C₄²×C₁₄₉	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₁₄₉	—	2	2	no	—
69	#103×C₁₄₉	—	2	8	no	—
70	C₂²⋊C₈×C₁₄₉	C₂³	1	4	yes	—
71	C₄×C₈×C₁₄₉	—	2	2	no	—
72	#95×C₁₄₉	—	2	4	no	—
73	#95×C₁₄₉	C₂³	1	2	yes	—
74	C₂⁴×C₁₄₉	—	2	4	no	—
75	C₂⁴×C₁₄₉	C₂×D₄	1	2	yes	—
76	#41×C₁₄₉	—	4	16	no	—
77	#41×C₁₄₉	—	4	4	no	—
78	#41×C₁₄₉	—	4	4	no	—
79	C₂×Q₈×C₁₄₉	—	2	2	no	—
80	C₂×Q₈×C₁₄₉	—	2	4	no	—
81	C₂×Q₈×C₁₄₉	—	8	2	no	—
82	C₂×D₄×C₁₄₉	—	2	8	no	—
83	C₂×D₄×C₁₄₉	—	2	4	no	—
84	C₂×D₄×C₁₄₉	—	2	4	no	—
85	C₂×D₄×C₁₄₉	—	2	2	no	—
86	C₂×D₄×C₁₄₉	—	2	2	no	—
87	C₂×D₄×C₁₄₉	—	2	2	no	—
88	C₂×D₄×C₁₄₉	—	2	2	no	—
89	C₂×D₄×C₁₄₉	—	4	16	no	—
90	C₂×D₄×C₁₄₉	—	4	8	no	—
91	C₂×D₄×C₁₄₉	—	4	8	no	—
92	C₂×D₄×C₁₄₉	—	8	4	no	—
93	C₂×D₄×C₁₄₉	SD₁₆	1	4	yes	complemented
94	C₂×D₄×C₁₄₉	C₂×D₄	1	4	yes	—
95	C₂²×C₄×C₁₄₉	—	2	4	no	—
96	C₂²×C₄×C₁₄₉	—	2	2	no	—
97	C₂²×C₄×C₁₄₉	—	2	4	no	—
98	C₂²×C₄×C₁₄₉	—	2	2	no	—
99	C₂²×C₄×C₁₄₉	—	2	2	no	—
100	C₂²×C₄×C₁₄₉	—	2	2	no	—
101	C₂²×C₄×C₁₄₉	—	4	4	no	—
102	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₄₉	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₄₉	C₂⁴	1	1	yes	characteristic
106	SD₁₆×C₁₄₉	—	8	8	no	—
107	C₂×C₈×C₁₄₉	—	2	4	no	—
108	C₄⋊C₄×C₁₄₉	—	2	4	no	—
109	C₄⋊C₄×C₁₄₉	—	2	2	no	—
110	C₄⋊C₄×C₁₄₉	—	2	2	no	—
111	C₄⋊C₄×C₁₄₉	—	4	2	no	—
112	C₄⋊C₄×C₁₄₉	—	4	1	no	—
113	C₄⋊C₄×C₁₄₉	—	4	2	no	—
114	C₄⋊C₄×C₁₄₉	—	4	1	no	—
115	C₄⋊C₄×C₁₄₉	C₂×D₄	1	4	yes	—
116	C₂²⋊C₄×C₁₄₉	—	2	8	no	—
117	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
118	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
119	C₂²⋊C₄×C₁₄₉	—	2	4	no	—
120	C₂²⋊C₄×C₁₄₉	—	8	4	no	—
121	C₄²×C₁₄₉	—	4	2	no	—
122	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
123	C₄²×C₁₄₉	C₂×D₄	1	2	yes	—
124	C₂³×C₁₄₉	—	2	2	no	—
125	C₂³×C₁₄₉	—	2	2	no	—
126	C₂³×C₁₄₉	—	2	4	no	—
127	C₂³×C₁₄₉	—	4	2	no	—
128	C₂³×C₁₄₉	—	4	2	no	—
129	C₂³×C₁₄₉	—	4	8	no	—
130	C₂³×C₁₄₉	—	8	4	no	—
131	C₂³×C₁₄₉	—	8	4	no	—
132	C₂³×C₁₄₉	C₂×SD₁₆	1	4	yes	—
133	C₂³×C₁₄₉	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₁₄₉	—	4	8	no	—
135	Q₈×C₁₄₉	—	4	4	no	—
136	D₄×C₁₄₉	—	2	8	no	—
137	D₄×C₁₄₉	—	4	4	no	—
138	D₄×C₁₄₉	—	4	16	no	—
139	D₄×C₁₄₉	—	4	4	no	—
140	D₄×C₁₄₉	—	4	4	no	—
141	D₄×C₁₄₉	—	4	4	no	—
142	D₄×C₁₄₉	—	4	4	no	—
143	D₄×C₁₄₉	—	8	4	no	—
144	C₂×C₄×C₁₄₉	—	2	2	no	—
145	C₂×C₄×C₁₄₉	—	2	2	no	—
146	C₂×C₄×C₁₄₉	—	2	4	no	—
147	C₂×C₄×C₁₄₉	—	4	1	no	—
148	C₂×C₄×C₁₄₉	—	4	8	no	—
149	C₂×C₄×C₁₄₉	—	4	8	no	—
150	C₂×C₄×C₁₄₉	—	4	4	no	—
151	C₂×C₄×C₁₄₉	—	4	2	no	—
152	C₂×C₄×C₁₄₉	—	4	2	no	—
153	C₂×C₄×C₁₄₉	—	4	4	no	—
154	C₂×C₄×C₁₄₉	—	4	2	no	—
155	C₂×C₄×C₁₄₉	—	4	2	no	—
156	C₂×C₄×C₁₄₉	—	4	2	no	—
157	C₂×C₄×C₁₄₉	—	8	2	no	—
158	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
159	C₂×C₄×C₁₄₉	#120	1	2	yes	—
160	C₂×C₄×C₁₄₉	#120	1	1	yes	characteristic
161	C₂×C₄×C₁₄₉	C₂×SD₁₆	1	2	yes	—
162	C₂×C₄×C₁₄₉	AGL(1,ℤ/8)	1	2	yes	—
163	C₂×C₄×C₁₄₉	C₂²×D₄	1	2	yes	—
164	C₈×C₁₄₉	—	4	4	no	—
165	C₂²×C₁₄₉	—	2	1	no	—
166	C₂²×C₁₄₉	—	2	1	no	—
167	C₂²×C₁₄₉	—	2	4	no	—
168	C₂²×C₁₄₉	—	4	4	no	—
169	C₂²×C₁₄₉	—	4	2	no	—
170	C₂²×C₁₄₉	—	4	2	no	—
171	C₂²×C₁₄₉	—	4	4	no	—
172	C₂²×C₁₄₉	—	4	4	no	—
173	C₂²×C₁₄₉	—	4	4	no	—
174	C₂²×C₁₄₉	—	8	2	no	—
175	C₂²×C₁₄₉	—	16	8	no	—
176	C₂²×C₁₄₉	C₂×#120	1	1	yes	characteristic
177	C₂²×C₁₄₉	C₂²×SD₁₆	1	1	yes	characteristic
178	C₂²×C₁₄₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₄×C₁₄₉	—	2	1	no	—
180	C₄×C₁₄₉	—	2	2	no	—
181	C₄×C₁₄₉	—	4	4	no	—
182	C₄×C₁₄₉	—	4	2	no	—
183	C₄×C₁₄₉	—	8	2	no	—
184	C₄×C₁₄₉	—	8	2	no	—
185	C₄×C₁₄₉	#450	1	4	yes	—
186	C₄×C₁₄₉	#455	1	2	yes	—
187	C₂×C₁₄₉	—	2	1	no	—
188	C₂×C₁₄₉	—	2	1	no	—
189	C₂×C₁₄₉	—	4	4	no	—
190	C₂×C₁₄₉	—	8	4	no	—
191	C₂×C₁₄₉	C₂×#450	1	1	yes	characteristic
192	C₂×C₁₄₉	C₂×#455	1	1	yes	characteristic
193	C₂×C₁₄₉	#3027	1	1	yes	characteristic
194	#18388	C₁₄₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₁₄₉	#18388	1	1	yes	characteristic, direct product factor, Sylow
196	#3496	C₂×C₁₄₉	1	1	yes	characteristic
197	#3206	C₂×C₁₄₉	1	2	yes	complemented
198	#2563	C₂×C₁₄₉	1	1	yes	characteristic, complemented
199	#1601	C₂×C₁₄₉	1	8	yes	complemented
200	#1502	C₂×C₁₄₉	1	2	yes	complemented
201	#1460	C₂×C₁₄₉	1	1	yes	characteristic, complemented
202	C₂×H(5,𝔽₂)	—	2	1	no	—
203	#547	—	2	2	no	—
204	#546	—	2	4	no	—
205	D₄²	—	2	2	no	—
206	#537	—	2	1	no	—
207	#534	C₂²×C₁₄₉	1	4	yes	—
208	#532	C₂²×C₁₄₉	1	2	yes	—
209	C₂×C₄⋊Q₈	C₂²×C₁₄₉	1	1	yes	characteristic, complemented
210	C₂×#121	—	2	2	no	—
211	C₂×C₄×D₄	C₂²×C₁₄₉	1	1	yes	characteristic
212	#492	—	2	2	no	—
213	#487	—	2	2	no	—
214	#461	—	2	4	no	—
215	#448	C₂²×C₁₄₉	1	8	yes	complemented
216	#431	C₂²×C₁₄₉	1	2	yes	complemented
217	#393	C₂²×C₁₄₉	1	4	yes	complemented
218	#390	—	2	1	no	—
219	#382	—	2	1	no	—
220	#380	—	2	2	no	—
221	C₄×C₄⋊C₄	C₂²×C₁₄₉	1	1	yes	characteristic, complemented
222	#327	C₂²×C₁₄₉	1	8	yes	complemented
223	#323	C₂²×C₁₄₉	1	4	yes	complemented
224	H(5,𝔽₂)	—	4	4	no	—
225	H(5,𝔽₂)	—	4	4	no	—
226	C₂×#41	—	2	4	no	—
227	C₂×#41	—	2	2	no	—
228	C₂²×Q₈	C₂³×C₁₄₉	1	2	yes	—
229	C₂²×D₄	—	2	4	no	—
230	C₂²×D₄	—	2	4	no	—
231	C₂²×D₄	—	2	2	no	—
232	C₂²×D₄	D₄×C₁₄₉	1	1	yes	characteristic
233	C₂³×C₄	D₄×C₁₄₉	1	2	yes	—
234	C₂×SD₁₆	—	2	8	no	—
235	C₄⋊Q₈	—	2	2	no	—
236	C₄⋊Q₈	—	2	2	no	—
237	C₄⋊Q₈	D₄×C₁₄₉	1	2	yes	—
238	#127	D₄×C₁₄₉	1	2	yes	—
239	#124	—	2	2	no	—
240	#123	—	2	8	no	—
241	C₂²⋊Q₈	—	2	4	no	—
242	#121	—	2	4	no	—
243	#121	—	2	4	no	—
244	#121	—	2	4	no	—
245	#121	—	2	2	no	—
246	#121	—	2	4	no	—
247	#121	C₂³×C₁₄₉	1	4	yes	—
248	#120	—	2	8	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	—	2	2	no	—
251	C₄×D₄	—	2	2	no	—
252	C₄×D₄	D₄×C₁₄₉	1	4	yes	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	D₄×C₁₄₉	1	1	yes	characteristic
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₂²⋊C₄	—	2	4	no	—
260	C₂×C₂²⋊C₄	C₂³×C₁₄₉	1	2	yes	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	C₂³×C₁₄₉	1	1	yes	characteristic
263	C₄⋊C₈	—	2	2	no	—
264	#103	—	2	8	no	—
265	C₂²⋊C₈	C₂³×C₁₄₉	1	4	yes	—
266	C₄×C₈	—	2	2	no	—
267	#95	—	2	4	no	—
268	#95	C₂³×C₁₄₉	1	2	yes	—
269	C₂⁴	—	2	4	no	—
270	C₂⁴	C₂×D₄×C₁₄₉	1	2	yes	—
271	#41	—	4	16	no	—
272	#41	—	4	4	no	—
273	#41	—	4	4	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	4	no	—
276	C₂×Q₈	—	8	2	no	—
277	C₂×D₄	—	2	8	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	4	16	no	—
285	C₂×D₄	—	4	8	no	—
286	C₂×D₄	—	4	8	no	—
287	C₂×D₄	—	8	4	no	—
288	C₂×D₄	SD₁₆×C₁₄₉	1	4	yes	complemented
289	C₂×D₄	C₂×D₄×C₁₄₉	1	4	yes	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	4	4	no	—
297	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₁₄₉	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₁₄₉	1	1	yes	characteristic
300	C₂²×C₄	C₂⁴×C₁₄₉	1	1	yes	characteristic
301	SD₁₆	—	8	8	no	—
302	C₂×C₈	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	C₂×D₄×C₁₄₉	1	4	yes	—
311	C₂²⋊C₄	—	2	8	no	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₂²⋊C₄	—	2	4	no	—
314	C₂²⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	8	4	no	—
316	C₄²	—	4	2	no	—
317	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
318	C₄²	C₂×D₄×C₁₄₉	1	2	yes	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	4	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	8	no	—
325	C₂³	—	8	4	no	—
326	C₂³	—	8	4	no	—
327	C₂³	C₂×SD₁₆×C₁₄₉	1	4	yes	—
328	C₂³	C₂²×D₄×C₁₄₉	1	1	yes	characteristic
329	Q₈	—	4	8	no	—
330	Q₈	—	4	4	no	—
331	D₄	—	2	8	no	—
332	D₄	—	4	4	no	—
333	D₄	—	4	16	no	—
334	D₄	—	4	4	no	—
335	D₄	—	4	4	no	—
336	D₄	—	4	4	no	—
337	D₄	—	4	4	no	—
338	D₄	—	8	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	8	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
354	C₂×C₄	#120×C₁₄₉	1	2	yes	—
355	C₂×C₄	#120×C₁₄₉	1	1	yes	characteristic
356	C₂×C₄	C₂×SD₁₆×C₁₄₉	1	2	yes	—
357	C₂×C₄	AGL(1,ℤ/8)×C₁₄₉	1	2	yes	—
358	C₂×C₄	C₂²×D₄×C₁₄₉	1	2	yes	—
359	C₈	—	4	4	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	4	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	4	2	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	16	8	no	—
371	C₂²	C₂×#120×C₁₄₉	1	1	yes	characteristic
372	C₂²	C₂²×SD₁₆×C₁₄₉	1	1	yes	characteristic
373	C₂²	C₂×AGL(1,ℤ/8)×C₁₄₉	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	2	no	—
378	C₄	—	8	2	no	—
379	C₄	—	8	2	no	—
380	C₄	#450×C₁₄₉	1	4	yes	—
381	C₄	#455×C₁₄₉	1	2	yes	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	4	4	no	—
385	C₂	—	8	4	no	—
386	C₂	C₂×#450×C₁₄₉	1	1	yes	characteristic
387	C₂	C₂×#455×C₁₄₉	1	1	yes	characteristic
388	C₂	#3027×C₁₄₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₄₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₄₉
prime radical	#3496×C₁₄₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₄₉ ◁ C₂×C₄²×C₁₄₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. #3206×C₁₄₉	C₂	semidirect
3. #2563×C₁₄₉	C₂	semidirect
4. #1601×C₁₄₉	C₂	semidirect
5. #1502×C₁₄₉	C₂	semidirect
6. #1460×C₁₄₉	C₂	semidirect
14. C₂×C₄⋊Q₈×C₁₄₉	C₂²	semidirect
20. #448×C₁₄₉	C₂²	semidirect
21. #431×C₁₄₉	C₂²	semidirect
22. #393×C₁₄₉	C₂²	semidirect
26. C₄×C₄⋊C₄×C₁₄₉	C₂²	semidirect
27. #327×C₁₄₉	C₂²	semidirect
28. #323×C₁₄₉	C₂²	semidirect
93. C₂×D₄×C₁₄₉	SD₁₆	semidirect
194. #18388	C₁₄₉	direct (N × H)
195. C₁₄₉	#18388	direct (N × H)
197. #3206	C₂×C₁₄₉	semidirect
198. #2563	C₂×C₁₄₉	semidirect
199. #1601	C₂×C₁₄₉	semidirect
200. #1502	C₂×C₁₄₉	semidirect
201. #1460	C₂×C₁₄₉	semidirect
209. C₂×C₄⋊Q₈	C₂²×C₁₄₉	semidirect
215. #448	C₂²×C₁₄₉	semidirect
216. #431	C₂²×C₁₄₉	semidirect
217. #393	C₂²×C₁₄₉	semidirect
221. C₄×C₄⋊C₄	C₂²×C₁₄₉	semidirect
222. #327	C₂²×C₁₄₉	semidirect
223. #323	C₂²×C₁₄₉	semidirect
288. C₂×D₄	SD₁₆×C₁₄₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#3496×C₁₄₉	2
#3206×C₁₄₉	2
#2563×C₁₄₉	2
#1601×C₁₄₉	2
#1502×C₁₄₉	2
#1460×C₁₄₉	2
#18388	149

Subgroups — C149×#18388 #49197337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₄₉×#18388 #49197337